Solution to "The First Pie Thrown"

Because there are 3 men, 3 women, and at least 1 same sex couple (clue 6), there are two same sex couples.

Mr. Lemmon isn't Lance (clue 2), Abby (gender), Barbara (gender), Chad (clue 7), or Wilma (gender), he is Tom.

Since Tom is Mr. Lemmon and Chad isn't Mr. White (clue 11), Lance is Mr. White and Chad is Mr. Tan.

Since Lance White has a female partner (clue 8), Tom Lemmon and Chad Tan are romantic partners and therefore didn't throw pies at each other (clue 3).

Since Abby isn't Ms. Brown (clue 12) and Barbara isn't Ms. Brown (clue 2), Wilma is Ms. Brown.

Since Abby has to be either Ms. Azure or Ms. Cherry, she can't be the one who threw the cherry cream pie (clue 10), and therefore the one who was hit by the blueberry cream pie (clue 9).

Since Lance White isn't Mr. Lemmon (clue 2), the one who threw the chocolate cream pie (clue 8), Ms. Brown (gender), the one who threw the vanilla cream pie (clue 4), or Chad, Lance White is the one who was hit with a lemon cream pie, (clue 7).

Since Chad Tan isn't Lance, Abby's partner (previous conclusion), Barbara, Tom, or the one hit with a blueberry cream pie (previous conclusion), Chad Tan threw the cherry cream pie (clue 9).

Since Chad Tan didn't throw the lemon cream pie (previous conclusion) and Lance White was hit with the lemon cream pie (previous conclusion), Lance White isn't the one who was hit by Chad Tan.

Since Lance White didn't throw the cherry cream pie (previous conclusion), isn't Ms Azure or Ms. Cherry (gender) isn't Mr. Tan's partner (previous conclusion), or the one hit by Mr. Tan (clue 11 and previous conclusion), Lance White is the one who threw the coconut cream pie.

Since Wilma Brown isn't the one who threw the cherry cream pie (previous conclusion), isn't Ms. Azure or Cherry, isn't Mr. Tan's partner, or isn't the one that threw the coconut cream pie, Wilma Brown is the one hit by Mr. Tan (clue 10) and therefore the one hit by a cherry cream pie (previous conclusion).

Since Barbara Azure isn't Mr. Lemmon (gender), Ms. Brown (previous conclusion), the one hit with the lemon cream pie (previous conclusion), the one who threw the vanilla cream pie (clue 12), or Chad, Barbara Azure threw the chocolate cream pie.

Since Barbara Azure wasn't hit with the chocolate cream pie (which she threw), the cherry cream pie (previous conclusion), the lemon cream pie (previous conclusion), the blueberry pie (clues 5 and 9), or the coconut cream pie (clue 3), she was hit with the vanilla cream pie by Abby (clue 12)

Since Abby isn't Lance, the one who threw the cherry cream pie (previous conclusion), Abby's partner, Barbara, or Tom, Abby is the one hit with the blueberry cream pie.

Since Wilma didn't throw the cherry cream pie (previous conclusion). The chocolate cream pie (clue 7), the vanilla cream pie (clue 7), the coconut cream pie, the blueberry cream pie (clue 3), Wilma hit Lance with the lemon cream pie.

Since Tom didn't throw the cherry cream pie (previous conclusion), the chocolate cream pie (clue 7), the vanilla cream pie (clue 7), the lemon cream pie (previous conclusion and clue 5), or the coconut cream pie (previous conclusion), Tom threw the blueberry cream pie at Abby

Since Chad wasn't hit with the lemon cream pie (previous conclusion), the blueberry cream pie (previous conclusion), the cherry cream pie (previous conclusion), the vanilla cream pie (previous conclusion), or the coconut cream pie (clue 5), he was hit with the chocolate cream pie thrown by Barbara.

Since Wilma hit Lance, Tom hit Abby, Abby hit Barbara, Barbara hit Chad, and Chad hit Wilma (all previous conclusions), Lance hit Tom with a coconut cream pie.

In conclusion:

Participant Partner Pie Thrown Target
Wilma Brown Abby Cherry Lemon Cream Lance White
Lance White Barbara Azure Coconut Cream Tom Lemmon
Tom Lemmon Chad Tan Blueberry Cream Abby Cherry
Abby Cherry Wilma Brown Vanilla Cream Barbara Azure
Barbara Azure Lance White Chocolate Cream Chad Tan
Chad Tan Tom Lemmon Cherry Cream Wilma Brown